bus transportation

Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1329 – 1340

1877-0428 © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license.Selection and peer-review under responsibility of Chinese Overseas Transportation Association (COTA).doi: 10.1016/j.sbspro.2013.08.151

ScienceDirect

13th COTA International Conference of Transportation Professionals (CICTP 2013)

Cen ZHANG a, Jing TENG b* a Ph.D. candidate, Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, 4800 Caoan Highway,

Shanghai 201804, P.R.China. E-mail:[email protected] b Associate Professor, Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, 4800 Caoan

Highway, Shanghai 201804, P.R.China. E-mail: [email protected]

Abstract

Since dwell time usually takes a large part of bus travel time, the large variability in dwell time always makes accurate prediction of arrival time\travel time difficult. On the other hand, Automatic Vehicle Location (AVL) and Automatic Passengers Counters (APC) systems are increasingly implemented for transit operation, which yield a vast amount of real time data. The emphasis of this research is to develop a bus dwell time model based on AVL and APC dynamic data, which is capable of providing real time information on bus arrival times. This model can be used for stop-based control strategies as well. The dwell time model established in this paper not only includes the number of passengers boarding and alighting, but also considers secondary factors like crowding and fare type. The number of boarding and alighting passengers is estimated by passenger arrival rate, bus headway, and capacity. Collection method, service mode, capacity restriction and occupancy of the vehicle are all taken into account in the model. Furthermore, the model is validated with the data of bus line Jiading 3 in Shanghai, China. It is compared with two previously developed models for the same route in four data sets. The results indicate that the models can be well applied in high demanded urban bus lines, especially in presence of high occupancy of vehicles. Since the effectiveness of estimation models is verified by statistical analysis methods, it will help in obtaining a reliable algorithm which can be adopted for bus arrival time/travel time prediction and assessing transit stop-based dynamic control actions.

© 2013 The Authors. Published by Elsevier B.V. Selection and/or peer-review under responsibility of Chinese Overseas Transportation Association (COTA).

Keyword: arrival time prediction,automatic vehicle location, automatic passengerr counter,dwell time, capacity limits, in-vehicle occupancy

*Jing Teng. Tel.: +086-021-69583001; fax: +086-021-69583001. E-mail [email protected]

Available online at www.sciencedirect.com

© 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license.Selection and peer-review under responsibility of Chinese Overseas Transportation Association (COTA).

http://creativecommons.org/licenses/by-nc-nd/3.0/

http://creativecommons.org/licenses/by-nc-nd/3.0/

1330 Cen Zhang and Jing Teng / Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1329 – 1340

1. Introduction

Many countries have been facing increasing challenges in terms of traffic congestion and people are encouraged to adopt public rather than private transportation, thus helping in relieving congestion and associated problems. Several measures have been attempted all over the world, including China, to make public transport bus services more attractive to the community. One such measure is to provide accurate bus arrival information to users pre-trip and in bus stops to minimize wait time. Therefore, a growing interest has been developing in bus arrival time/travel time prediction.

Since dwell time takes up a significant fraction of the trip time along a serviced bus line, variation of dwell time may largely affect the accuracy of travel time prediction. Most of the studies in the area of bus travel time prediction include bus dwell time implicitly in the link travel time. Indeed, running time in links and dwell time at stops are affected by different issues. Recently, the new approach is to divide the bus travel time into two components-running times and dwell time at bus stops and analysis each separately.

Bus dwell time Estimation and Prediction as the base of bus travel time prediction, can also be used for the application of stop-based control strategies. According the dwell time prediction, and the current traffic conditions and bus headway, the control strategy in the station can be selected and adjusted accurately.

However, dynamic dwell time prediction is a challenging task, since there are so many factors contributing to dwell time. The Transit Capacity and Quality of Service Manual defined bus dwell time as the duration of time of the transit vehicle stopped for serving passengers. It includes the total passenger boarding and alighting times and the time needed for the bus to open and close doors. As to a specific bus, the door opening time and closing times are generally fixed, boarding and alighting times may vary in different condition; therefore, the number of boarding and alighting at bus stops are likely the most significant factors causing dwell time variations. Factors contributing to dwell time also include the configuration and occupancy of the bus, the method of fare collection, service mode.

In fact, things become a little different in china. Compared with the developed countries, the high population density in the urban city leads to high passenger demand for transit. In the peak hours, the phenomenon that vehicles are so crowd that people can’t get on and off easily even sometimes passengers have to wait for the next bus since there is no room for one more. All these conditions that often occur in China, may cause the large dwell time prediction error to great extent. And the characteristics of passengers in china are quite different from the other countries.

In other aspect, due to Automatic Vehicle Location (AVL) and Automatic Passengers Counters (APC) systems have been increasingly implemented for transit operation, a vast amount of potentially real time data could be obtained from these systems. These make the dynamic dwell time prediction possible in the complex conditions.

Literature Review

Historically, various methods, such as historic and real-time approaches, machine learning techniques (artificial neural network, support vector machines), model based approaches (Kalman filtering) and statistical methods (regression analysis, time-series), have been adopted in the prediction of bus arrival time.

It can be seen that, no matter what methods are introduced, in the most of the studies the data of travel time instead of dwell time at stops and link running time was used. It means that dwell time is included in travel time. However, running time in links and dwell time at stops are affected by different issues.

Although, the literature available on travel time or arrival time prediction taking dwell time into account is exiguous before 2003.In recent years, a few study are trying to predict arrival time through separating link running time and dwell time. Shalaby and Farhan (2003) used data collected with automatic vehicle location (AVL) and automatic passenger counters (APC) for the prediction of bus arrival time. They developed a model for bus arrival prediction which consisted of two Kalman filters, one for predicting the travel time and the other for predicting the dwell time as a function of the number of passengers alighting and boarding the bus at each bus stop. Padmanaban and Vanajakshi (2003) tried to explicitly incorporate the dwell time associated with the total


travel times of the buses under heterogeneous traffic conditions. In these researches, estimation models of running time and dwell time model were established respectively. But only the number of passengers alighting and boarding was taken into account in the dwell time prediction.

In fact, dwell time is affected by many issues. In TCRP Report 100, the factors that affect dwell time consist of passenger boarding and alighting volumes, fare payment method, in-vehicle circulation, and stop spacing. Further studies find out more factors, such as the vehicle type, time of day, service type, stop location, weather condition and passenger behavior also have a great contribution to dwell time.

Among these factors, the passenger demand factor is agreed to be the principal determinant of dwell time and was analyzed most. In the most study, it is proportional to passenger boarding or alighting volume, or both. Levinson(1983) developed a linear regression model for dwell time estimation with the total number of boarding and alighting passengers. Guenthner and Sinha (1983) developed a natural logarithm model for dwell time estimation using the sum of boarding and alighting passengers as variable. Kittelson and Associates established a multivariate linear regression model considering boarding and alighting passengers as separate variables. Shalaby and Farhan (2003) assumed that boarding passengers at each bus stop have a more significant effect than alighting passengers on bus dwell time at that stop, and the model are only relative with boarding passengers.

Different countries have different traffic features. Emilio G. Moreno González (2012) proposed a bus dwell-time model contains the influence of occasional incidents in the boarding process in Madrid, Spain. And Akhilesh Koppineni developed bus arrival time prediction system prototype for the special traffic conditions in Indian, such as bus break down, congestion, overtaking, traffic jam, abrupt stoppage of services and unscheduled changes in routes. Very few bus arrival predictions have been carried out under China traffic conditions. Compared with the developed countries, the high population density in the urban city and the unstable passenger flow cause that in the peak hour the demand exceeds the capacity, high crowdedness level in vehicle extends the boarding and alighting time, and the capacity limits the number of boarding passengers. Thus, there is a need for models that can capture the special effect with little data requirement. This paper is aim at using AVL and APC data to estimate the dwell time in the arrival time prediction in china.

2. Data Collection

The data used for this study were collected from bus line Jiading 3 in Shanghai, China. The route length is approximately 6.4 km, spanning 17 bus stops in each direction, 4 of which are located at points of high passenger demand. And it has a high index of occupation, with a demand of more than 600 pax/h in each direction in rush hour.

All of the buses in line Jiading 3 are equipped with AVL but without APC. So the data of passengers were collected manually using on-board counting from 4:00 PM to 6:00 PM on April.7, April 14 and April 21, which are three successive Friday in 2012, with the records of 72 trips.

The vehicles on this route are high-floor buses and have 22 seat and two doors—the rear door is for alighting only, while boarding at the front door are permitted. Automatic fare collection system is used in the route, and passenger can pay by cash or IC card.

3. Model Development

As discussed already, most of the existing travel time prediction models include bus dwell time implicitly in the link travel time. The approach presented here is to divide the total travel time of a bus into two components – link running time and dwell time at bus stops. Only bus dwell times are modeled in this study. So it is assumed that real-time information on passenger boarding and alighting at bus stops and bus arrival and departure times is known from AVL and APC systems, and link running time prediction is accurate.

The passenger boarding and alighting time is the main part of dwell time. In order to predict the dwell time, the passenger boarding and alighting number should be predicted first. The model consists of two separate parts, passenger boarding and alighting prediction algorithm and bus dwell time estimation algorithm.


In order to better understand the prediction-modeling framework, the process of bus dwell time prediction is illustrated as follow: When bus k+1 leaves the stop n, the departure time k+1

,DTn is known from the AVL system. At

this instant, the next link running time k+1, 1RTn n and the predicted arrival time of the bus at the downstream bus

stop n+1( k+1+1,ATn ) will be predicted. Subsequently, k+1

1DTn will be estimated by the bus dwell time model, and k+1+1,DTn can be determined.

k,DTn

k+1,ATn

k+1,DTn

k,ATn

k+1,ATn

k+1,DTn

k+1+1,ATn

k+1+1,DTn

k, 1RTn n

k+1, 1RTn n

kDTnk+1DTn

k1DTn

k+11DTn

Fig. 1. Illustration of bus operation (buses from the same route)

3.1. Passenger boarding and alighting prediction algorithm

The first algorithm is “Passenger boarding and alighting Prediction Algorithm” which makes use of the historical data and the information of previous bus on the current day to predict the boarding and alighting Passengers. In the peak hour, some passengers can’t board the bus, since lack of enough space in the vehicle, was observed in the study. The capacity of buses has been considered in this algorithm. The boarding passengers can be predicted by the following expression:

1 11 1 1, 1, 1( )k k k k

n n n A n A nPb PT T R (1) Where:

11

knPb : predicted boarding passengers for bus (k+1) at stop ( n+1)

1n : predicted passenger arrival rate at stop (n+1) 1

1,k

n APT : predicted arrival time of bus (k+1) at stop (n+1)

1,k

n AT : actual arrival time of bus k at stop (n+1)

1, 1,k k

n A n APT T : predicted headway for bus k at stop n+1

1knR : predicted remain passengers after departure of bus k from stop n+1

The number of in-vehicle passengers can be calculated as: 1 1 1

k k k kn n n nN N b a (2)

Where: 1

knN : number of in-vehicle passengers for bus k after departure from stop n+1 knN : number of in-vehicle passengers for bus k after departure from stop n

1knb : actual boarding passengers for bus k at stop n+1


1kna : actual alighting passengers for bus k at stop n+1

Here, the parameter 1Skn is introduced in the model to indicate whether the capacity is reached.it is defined as:

1 1Sk kn k nC N (3)

Where: 1Sk

n : saturation of capacity for bus k after departure from stop n+1,if 1S 0kn ,it presented that the number of

passengers in the bus k reached the capacity; 1

knN : number of in-vehicle passengers for bus k after departure from stop n+1;

kC : Maximum number of passengers can be in the bus k; If passengers exceed the capacity of vehicle, there are remain passengers that have to wait for the next bus. The number of remain passengers can calculate as:

1 1 11

1

, 00, 0

k k kk n n nn k

n

Pb b SR

S (4)

Where: 1

knR : predicted remain passengers after departure of bus k from stop (n+1);

1knPb : predicted boarding passengers for bus(k+1) at stop( n+1);

1knb : actual boarding passengers for bus k at stop (n+1);

1Skn : saturation of capacity for bus k after departure from stop (n+1);

The number of the alighting passengers can be estimated by passengers in-vehicle:

1 11 1 1

k kn n nPa N (5)

Where: 11

knPa : predicted alighting passengers for bus(k+1) at stop( n+1)

11

knN : number of in-vehicle passengers for bus k after departure from stop n+1

1n : the predicted percentage of passengers alight at stop( n+1) And the parameter 1n is calculated by historic data as:

11

1

= nn m

in

(6)

i : the percentage of the alighting passengers in stop i takes up in history data statistic ; m: the total number of stops in the bus line ;

3.2. Bus dwell time estimation algorithm

Traditionally, the dwell time has been described as a linear function of the number of boarding and alighting passengers, affected by certain parameters that represent the speed of entry and exit, plus a dead time for opening and closing doors. Several functional forms have been suggested. A well-known American model is the Highway Capacity Manual (HCM) (12) and Transit Capacity and Quality of Service Manual (TCQSM) formulas for the dwell time (13):

d a a b b oct =P t +P t +t (7)


Where: dt :the dwell time in the bus stop;

aP : alighting passengers per bus through the busiest door (p);

at : alighting passenger service time (s/p);

bP : boarding passengers per bus through the busiest door (p);

bt : boarding passenger service time (s/p);

oct : the time for opening and closing doors(s). The European experience started with the work of Pretty and Russel (14) that proposed the following dwell

time model.

1 1max ;

m n

i ji j

T C a b (8)

Where: T :the dwell time in the bus stop;

ia : the time each passenger takes for alighting;

jb : the time each passenger takes for boarding; m: the number of alighting passengers; n : the number of boarding passengers; C: the dead time for opening and closing doors.

In China, manual collection and Automatic fare collection are adopted. Usually, in the bus payment system adopt manual collection on-board, which passengers are permitted board and alight through all the doors of the bus, Equation 7 is suitable for the service.

Automatic fare collection device (passengers can pay fare by cash or IC card) usually installed in the front door of bus, so passenger can only board through the front door and alight by the rear door. Equation 8 assumes that boarding and alighting passenger flows are distinct for the vehicles. In this condition that passengers can only board through one door and alight through the other door. So Equation 8 is applicable in the Automatic fare collection.

In the front situation, the dwell time can be estimated by the following expression: 1 1 1 1 1

1 1 1 1 1 1k k k k k

n n n n n nDT tb Pb ta Pa t (9) In the latter situation, the dwell time can be predicted by the following expression:

1 1 1 1 11 1 1 1 1 1( , )k k k k k

n n n n n nDT MAX ta Pb tb Pa t (10) In fact, crowding inside the bus will impact passenger activity when the passengers on board (causing the

crowded situation) are on the bus upon arrival and departure from the stop. The crowding effect inside the bus is considered in this model. Usually, the more crowd in the bus, longer the average alighting and boarding time per passenger is.

In order to analysis the crowding in the bus impact on alighting time per passenger and boarding time per passenger, this paper defines the crowding rate as follow:

1 11 1 +1 +1 +1( ) / ( )k k

n n k k kN S C S (11) Where:

11

kn : the crowding rate in the vehicle k+1 at the stop n+1;

+1kS :the number of seat in the vehicle k+1; Here, a time correction item is introduced to represent the impact of the crowdedness:


1 11 11

1 11

( - ), - 0

, - 0

k kb n b n bk

n kn b

tb mtb

tb (12)

1 11 11

1 11

- , - 0

, - 0

k ka n a n ak

n kn a

ta mta

ta (13)

Where: 11

kntb :average boarding time for the vehicle k+1 at stop n+1;

tb : average boarding time per passenger b : the crowding rate begins to affect passengers’ boarding time

bm : boarding compensation coefficient; 11

knta : average alighting time for the vehicle k+1 at stop n+1;

ta :average alighting time per passenger; am :alighting compensation coefficient;

a :the crowding rate begins to affect passengers’ alighting time

4. Model Performance Evaluation

In order to assess the predictive performance of the bus dwell time model, it is compared with two previously developed models for the same route. Model A which only takes boarding passengers into account is:

1 1 11 +1 1 +1 1, 1,+ ( )k k k k

n n n n n A n ADT t tb PT T The Model B considers the effect of both boarding and alighting passengers is as the following form: .

1 1 1 1 11 +1 1 +1 1, 1, 1 1 1+max( ( ), ))k k k k k k

n n n n n A n A n n nDT t tb PT T ta N The Model C is the one proposed in this paper, which considers the effect of crowdedness in vehicles and the

capacity limits. As mentioned earlier, the AVL and APC data for the study route were available for 3 days. The three models

were calibrated with using data of 2 days only, with the third day’s data held out for performance evaluation. The parameters are show in the table 1.And rages of values for the parameters observed in shanghai are: Dead time:3.0 to 12.0 seconds Alighting time: 1.0 to 3.0 seconds per passenger Boarding time: 1.6 to 8.0 seconds per passenger Average alighting time:1.13 Average boarding time:1.88 Average dead time:4.6 The average boarding time began to increase significantly after >0.3 while alighting time start to soar up

>0.4.

Table 1. The parameters of the models

Station NO n pass/s n tb s 1.88

1 0.013796 0.0000 ta s 1.13

2 0.009722 0.0000 tn s 4.6

3 0.005926 0.0009 C 60


4 0.011759 0.0234 S 22

5 0.013704 0.0478 mb 8.5

6 0.010833 0.0406 ma 2.4

7 0.010833 0.0977 b 0.3

8 0.000556 0.0201 a 0.4

9 0.003426 0.1105

10 0.002315 0.2996

11 0.004444 0.1627

12 0.015556 0.0699

13 0.000833 0.0164

14 0.001019 0.0072

15 0.000741 0.2284

16 0.000185 0.6137

17 0.000000 1.0000

18 0.012167 0.0000

19 0.015917 0.0011

20 0.007167 0.0096

21 0.001500 0.0011

22 0.001500 0.0065

23 0.002917 0.0857

24 0.004750 0.0747

25 0.012750 0.0897

26 0.003833 0.0479

27 0.004667 0.0444

28 0.004667 0.0960

29 0.002083 0.1729

30 0.004583 0.4389

31 0.001917 0.1919

32 0.000333 0.0913

33 0.000250 0.6482

34 0.000000 1.0000

Four testing data sets were used. The first set includes all test data, while the data are divided into three

categories, corresponding to three different in-vehicle conditions: non-crowding, crowding and exceeding capacity. After calculation, all the necessary data required for model testing was extracted and analysed. Three


prediction error measurements were computed for all developed models to test the model performance. These error indices include: Mean absolute error ( mean ), which indicates the expected error as a fraction of the measurement

1=mean true predt

X t X tN

Root mean squared error ( rs ), which captures large prediction errors

21Nrs true pred

tX t X t

Maximum absolute error ( max ), which capture the maximum prediction error

max max true predX t X t

Where: N: the number of samples; Xtrue (t): measured value at time t; Xpred (t) :predicted value at time t;

Here absolute error instead of relative error are used to indicate the performance, since the predicted value of dwell time is used to calculate the arrival time or travel time, absolute error can reflect the effect of accuracy in the arrival time/travel time prediction directly. Sometimes relative error is large, while absolute error is low, it can affect the accuracy of arrival time/travel time prediction little. Three absolute error indicators were selected for evaluation of performance

Table 2 shows the three error measures mean , rs , max for the test data, while Figure 2 (a,b,c) summarize the performance of the three prediction models for each condition. Obviously, the lower the error is, the better the model performance is.

5. Analysis and Results

The results summarized in Table 3, it shows that for all the conditions the model C provides the minimum value for the error measures mean , rs , max pointing to the fact that its performance was the best compared with the other models, except for the uncrowned condition where model B and C have the same performance.

Table 2 and Figure 2 (a,b,c,d) show there is no significant difference in the performance of the three models for the non-crowding scenario, but In general, the model C always gives lower value for the absolute error indices and shows the best prediction performance in all three conditions.

In the non-crowding scenario, model C was almost the same as model B, there were no difference in the results however, it showed superior performance to the other models in the crowding and the exceeding capacity scenarios, the value of rs which reflect large prediction errors and max which capture the maximum prediction error were much lower than model B and A. It means that in the latter two cases, the large errors can be reduced effectively. And in fact, large errors always appeared in the latter two conditions. Due to the uncertain behaviour of the passengers and driver, the dwell time forecasting can’t be so accurate. However, large errors may largely affect the arrival time/travel time prediction. Reducing large errors can effectively improve the precision of prediction. And in the most conditions, compared with A, the model B had better performance. It shows that taking both alighting and boarding passengers into account makes contribute to improve the accuracy.

In a word, performance of the model proposed in this paper was similar to the model B in the condition without crowding in vehicle, but it showed superior performance to the other models in the crowding and the capacity limits scenarios. These results showed the superior performance of the model C compared with other prediction models in terms of the absolute error, and it also demonstrates how this model can capture dynamic changes due to different bus operation characteristics at stops.


Table 2. Absolute error results of the prediction models

(a) (b)

(c) (d)

Fig. 2. Absolute error results of the prediction models

6. Conclusion

Travel time/arrival time prediction systems are predominantly found in many countries for many years and are based on historic data base or travel time patterns. One of the main challenges involved in bus travel time or arrival time prediction. Most of the reported studies in the area of bus travel time prediction, the new approach recently is to divide the total travel time into two components - running time and dwell time at bus stops, and analysis them separately. However, the studies before don’t take crowdedness and capacity limits into account, which are the major features in China. This paper proposes the model that is suitable in the conditions here.

model

All

(360 Predictive values

Non-crowding

(207 Predictive values)

Crowding

(141 Predictive values)

Exceeding capacity

(12 Predictive values

mean rt max mean rt max mean rt max mean rt max

A 4.58 6.78 32.2 4.11 6.58 20.4 5.21 5.78 32.2 5.29 7.47 26.7

B 4.19 6.42 32.2 4.03 6.52 20.4 4.33 5.22 32.2 5.31 5.75 26.7

C 3.96 5.98 20.4 4.03 6.52 20.4 3.85 4.32 16.8 4.04 4.19 17.9


In conclusion, the models proposed before to predict bus dwell time and models proposed in this research can both predict the dwell time with a acceptable err. However, inclusion of other factors like service type, capacity limits, fare collection methods, crowdedness in-vehicle, will increase the Accuracy of the bus dwell time prediction.

The model C includes these factors can provide better estimates in the high in-vehicle occupancy condition, which conforms to the situation of China's urban transit. However, calibration of the model C would be required to determine the model parameters to suit the existing condition .So the model B, which has less parameter, is better in the line that seldom with high occupancy in the vehicle.

Since the model for this research was developed based on AVL and APC data, lack of APC counter in the bus, the data are all collected by manual. Indeed, manual collected data and APC data are not totally same, that may affect the result of the prediction. And for engineering practice the usefulness of the dwell time model, the dynamic real-time testing with AVL and APC data, which have become critical issues in China, is necessary.

Because dwell time is predicted separately and its effect on bus arrival times at downstream stops is accounted for, the model also can be used for assessing transit stop-based dynamic control actions.

The dwell time model, only a part of the arrival time prediction models, developed based on data from one bus route in Shanghai. Some more different lines need be tested to increase the Reliability of the model.

Further work can improve the model developed here in several ways. Better representative distributions of passenger arrivals at bus stops could be attempted instead of the implied uniform distribution. What’s more, according to the characteristic of different stations, the parameters of stations can be set separately. And in the observation, other factors such as bunching phenomenon can affect the dwell time. The modify items for these factors can be added in the model in the future research.

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 61174185) and the Fundamental Research Funds for the Central Universities. The authors will also owe their great appreciation to Advanced Public Transit System laboratory of Tongji University for assistant in data collection.

References

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